Number Of Crossovers Research Articles

MSH2 shapes the meiotic crossover landscape in relation to interhomolog polymorphism in Arabidopsis

During meiosis, DNA double‐strand breaks undergo interhomolog repair to yield crossovers between homologous chromosomes. To investigate how interhomolog sequence polymorphism affects crossovers, we sequenced multiple recombinant populations of the model plant Arabidopsis thaliana. Crossovers were elevated in the diverse pericentromeric regions, showing a local preference for polymorphic regions. We provide evidence that crossover association with elevated diversity is mediated via the Class I crossover formation pathway, although very high levels of diversity suppress crossovers. Interhomolog polymorphism causes mismatches in recombining molecules, which can be detected by MutS homolog (MSH) mismatch repair protein heterodimers. Therefore, we mapped crossovers in a msh2 mutant, defective in mismatch recognition, using multiple hybrid backgrounds. Although total crossover numbers were unchanged in msh2 mutants, recombination was remodelled from the diverse pericentromeres towards the less‐polymorphic sub‐telomeric regions. Juxtaposition of megabase heterozygous and homozygous regions causes crossover remodelling towards the heterozygous regions in wild type Arabidopsis, but not in msh2 mutants. Immunostaining showed that MSH2 protein accumulates on meiotic chromosomes during prophase I, consistent with MSH2 regulating meiotic recombination. Our results reveal a pro‐crossover role for MSH2 in regions of higher sequence diversity in A. thaliana.

Excess crossovers impede faithful meiotic chromosome segregation in C. elegans.

During meiosis, diploid organisms reduce their chromosome number by half to generate haploid gametes. This process depends on the repair of double strand DNA breaks as crossover recombination events between homologous chromosomes, which hold homologs together to ensure their proper segregation to opposite spindle poles during the first meiotic division. Although most organisms are limited in the number of crossovers between homologs by a phenomenon called crossover interference, the consequences of excess interfering crossovers on meiotic chromosome segregation are not well known. Here we show that extra interfering crossovers lead to a range of meiotic defects and we uncover mechanisms that counteract these errors. Using chromosomes that exhibit a high frequency of supernumerary crossovers in Caenorhabditis elegans, we find that essential chromosomal structures are mispatterned in the presence of multiple crossovers, subjecting chromosomes to improper spindle forces and leading to defects in metaphase alignment. Additionally, the chromosomes with extra interfering crossovers often exhibited segregation defects in anaphase I, with a high incidence of chromatin bridges that sometimes created a tether between the chromosome and the first polar body. However, these anaphase I bridges were often able to resolve in a LEM-3 nuclease dependent manner, and chromosome tethers that persisted were frequently resolved during Meiosis II by a second mechanism that preferentially segregates the tethered sister chromatid into the polar body. Altogether these findings demonstrate that excess interfering crossovers can severely impact chromosome patterning and segregation, highlighting the importance of limiting the number of recombination events between homologous chromosomes for the proper execution of meiosis.

Natural variation in meiotic recombination rate shapes introgression patterns in intraspecific hybrids between wild and domesticated barley

Meiotic recombination rates vary considerably between species, populations and individuals. The genetic exchange between homologous chromosomes plays a major role in evolution by breaking linkage between advantageous and deleterious alleles in the case of introgressions. Identifying recombination rate modifiers is thus of both fundamental and practical interest to understand and utilize variation in meiotic recombination rates. We investigated recombination rate variation in a large intraspecific hybrid population (named HEB-25) derived from a cross between domesticated barley and 25 wild barley accessions. We observed quantitative variation in total crossover number with a maximum of a 1.4-fold difference between subpopulations and increased recombination rates across pericentromeric regions. The meiosis-specific α-kleisin cohesin subunit REC8 was identified as a candidate gene influencing crossover number and patterning. Furthermore, we quantified wild barley introgression patterns and revealed how local and genome-wide recombination rate variation shapes patterns of introgression. The identification of allelic variation in REC8 in combination with the observed changes in crossover patterning suggest a difference in how chromatin loops are tethered to the chromosome axis, resulting in reduced crossover suppression across pericentromeric regions. Local and genome-wide recombination rate variation is shaping patterns of introgressions and thereby directly influences the consequences of linkage drag.

Cooperative Task Assignment of a Heterogeneous Multi-UAV System Using an Adaptive Genetic Algorithm

The cooperative multiple task assignment problem (CMTAP) is an NP-hard combinatorial optimization problem. In this paper, CMTAP is to allocate multiple heterogeneous fixed-wing UAVs to perform a suppression of enemy air defense (SEAD) mission on multiple stationary ground targets. To solve this problem, we study the adaptive genetic algorithm (AGA) under the assumptions of the heterogeneity of UAVs and task coupling constraints. Firstly, the multi-type gene chromosome encoding scheme is designed to generate feasible chromosomes that satisfy the heterogeneity of UAVs and task coupling constraints. Then, AGA introduces the Dubins car model to simulate the UAV path formation and derives the fitness value of each chromosome. In order to comply with the chromosome coding strategy of multi-type genes, we designed the corresponding crossover and mutation operators to generate feasible offspring populations. Especially, the proposed mutation operators with the state-transition scheme enhance the stochastic searching ability of the proposed algorithm. Last but not least, the proposed AGA dynamically adjusts the number of crossover and mutation populations to avoid the subjective selection of simulation parameters. The numerical simulations verify that the proposed AGA has a better optimization ability and convergence effect compared with the random search method, genetic algorithm, ant colony optimization method, and particle search optimization method. Therefore, the effectiveness of the proposed algorithm is proven.

Exceptional Nuclease Resistance of Paranemic Crossover (PX) DNA and Crossover-Dependent Biostability of DNA Motifs

Nanometer-sized features and molecular recognition properties make DNA a useful material for nanoscale construction, but degradation in biological fluids poses a considerable roadblock to biomedical applications of DNA nanotechnology. Here, we report the remarkable biostability of a multistranded motif called paranemic crossover (PX) DNA. Compared to double stranded DNA, PX DNA has dramatically enhanced (sometimes >1000 fold) resistance to degradation by four different nucleases, bovine and human serum, and human urine. We trace the cause of PX's biostability to DNA crossovers, showing a continuum of protection that scales with the number of crossovers. These results suggest that enhanced biostability can be engineered into DNA nanostructures by adopting PX-based architectures or by strategic crossover placement.

A Non-Dominant Sorting Genetic Algorithm for Optimization of a Product Design and Selection of Its Suppliers

The aim of this paper is to address the problem of supplier selection in a context of an integrated product design. Indeed, the product specificities and the suppliers’ constraints are both integrated into product design phase. We consider the case of improving the design of an existing product and study the selection of its suppliers adopting a bi-objective optimization approach. Considering multi-products, multi-suppliers and multi-periods, the mathematical model proposed aims to minimize supplying, transport and holding costs of product components as well as quality rejected items. To solve the bi-objective problem, an evolutionary algorithm namely, non-dominant sorting genetic algorithm (NSGA-II) is employed. The algorithm provides a set of Pareto front solutions optimizing the two objective functions at once. Since parameters values of genetic algorithms have a significant impact on their efficiency, we have proposed to study the impact of each parameter on the fitness functions in order to determine the optimal combination of these parameters. Thus, a number of simulations evaluating the effects of crossover rate, mutation rate and number of generations on Pareto fronts are presented. To evaluate performance of the algorithm, results are compared to those obtained by the weighted sum method through a numerical experiment. According to the computational results, the non-dominant sorting genetic algorithm outperforms the CPLEX MIP solver in both solution quality and computational time.

Benign Regulation of the Astrocytic Phospholipase A2-Arachidonic Acid Pathway: The Underlying Mechanism of the Beneficial Effects of Manual Acupuncture on CBF.

BackgroundThe astrocytic phospholipase A2 (PLA2)-arachidonic acid (AA) pathway is crucial in understanding the reduction of cerebral blood flow (CBF) prior to cognitive deterioration. In complementary and alternative medicine, manual acupuncture (MA) is used as one of the most important therapies for Alzheimer’s disease (AD). The beneficial effects of MA on CBF were reported in our previous study. However, the underlying molecular mechanism remains largely elusive.ObjectiveTo investigate the effect of MA on the astrocytic PLA2-AA pathway in SAMP8 mice hippocampi.MethodsSAMP8 mice were divided into the SAMP8 control (Pc) group, the SAMP8 MA (Pm) group and the SAMP8 donepezil (Pd) group. SAMR1 mice were used as the SAMRl control (Rc) group. Mice in the Pd group were treated with donepezil hydrochloride at 0.65 μg/g. In the Pm group, MA was applied at Baihui (GV20) and Yintang (GV29) for 20 min. The above treatments were administered once a day for 26 consecutive days. The Morris water maze was applied to assess spatial learning and memory. Immunofluorescence staining, western blot and liquid chromatography-tandem mass spectrometry were used to investigate the expression of related proteins and measure the contents of the metabolic intermediates of the PLA2-AA pathway.ResultsCompared with that in the Rc group, the escape latency in the Pc group significantly increased (p < 0.01); whereas, the platform crossover number and percentage of time and swimming distance in the platform quadrant decreased (p < 0.01). The hippocampal expression of PLA2, cyclooxygenase-1, cytochrome P450 proteins 2C23 and the levels of AA, prostaglandin E2 and epoxyeicosatrienoic acids of the Pc group was drastically higher than that in the Rc group (p < 0.01). These changes were reversed by MA and donepezil (p < 0.01 or p < 0.05).ConclusionMA can effectively improve the learning and memory abilities of SAMP8 mice and has a negative regulatory effect on the PLA2-AA pathway. We propose that the increase of the arterial tone, which is induced by the inhibition of vasodilatory pathway, may be a reason for the beneficial effect of MA on CBF.

Toward Tailored Biostability of DNA Nanostructures

Predictive complementary nature of the base pairing allows us to use DNA for bottom-up construction of nanostructures. Recent studies have shown that DNA nanostructures could potentially have medical applications in drug delivery. For drug delivery to be successful, these DNA nanostructures must be able to reach the target site while withstanding the physiological conditions of the body. Thus, it is important to establish strategies to study and control the biostability of these nanocarriers in order to increase their resistance to degradation in vivo. Here we investigated the biostability of two different DNA nanostructures: (1) a four-sided, six-edged tetrahedron and (2) a multi stranded motif called paranemic crossover (PX). For the tetrahedron, we focused on the correlation between size and biostability and for the PX we focused on the relationship between number of crossovers and biostability. We designed three different-sized tetrahedrons with edges containing 13, 17 and 20 base pairs. Using DNase I and fetal bovine serum we found that there is no discernible pattern between biostability and size of DNA nanostructures. For the PX motif, we found that it exhibits dramatically higher resistance to nucleases compared to a regular duplex. In addition, PX motifs lacking a few crossovers showed monotonically decreasing stability, indicating that the number of crossovers in the structure has an effect on the nuclease resistance of the motif. Such systematic analysis of design and construction brings us one step closer to be able to build DNA nanostructures with real-life medical applications.

External Validation of the Subarachnoid Hemorrhage International Trialists (SAHIT) Predictive Model Using the Barrow Ruptured Aneurysm Trial (BRAT) Cohort.

The Subarachnoid Hemorrhage International Trialists (SAHIT) repository is a collection of randomized clinical trials, prospective observational studies, and hospital registries that was used to create a predictive model of unfavorable outcome/mortality following aneurysmal SAH. To externally validate the SAHIT model using Barrow Ruptured Aneurysm Trial (BRAT) data, which was not included in the SAHIT repository. This is a post hoc analysis of the prospective, randomized BRAT. Three models were created: (1) Core (age, hypertension, World Federation of Neurosurgical Societies grade), (2) neuroimaging (aneurysm size/location, Fisher score), and (3) full model (model 1 and 2 plus treatment type). The performance of the models was evaluated by measures of model discrimination (area under the curve [AUC]) and model calibration (goodness of fit test, calibration in-the-large, calibration slope). A total of 338 patients (average age 54 years; 67.7% good clinical grade; average aneurysm size 6.7 mm; 84.1% anterior circulation) were included. Due to a large number of crossovers, more aneurysms were clipped than coiled (67.5% vs 32.5%, respectively). A total of 10.1% of the patients died and 29.6% experienced an unfavorable outcome. For unfavorable outcome, the AUCs for the three models were: 0.728, 0.732, and 0.734, respectively. For mortality, the AUCs for the three models were: 0.721, 0.739, and 0.744, respectively. Overall, all models showed good calibration, and the measures of calibration fell within 95% CI of those produced in the SAHIT study. Using the BRAT data, we have externally validated the SAHIT model for predicting unfavorable outcome and mortality after SAH. The model may be used to counsel patients and families on prognosis following aneurysmal SAH.

Dmc1 is a candidate for temperature tolerance during wheat meiosis

Key messageThe meiotic recombination gene Dmc1 on wheat chromosome 5D has been identified as a candidate for the maintenance of normal chromosome synapsis and crossover at low and possibly high temperatures.We initially assessed the effects of low temperature on meiotic chromosome synapsis and crossover formation in the hexaploid wheat (Triticum aestivum L.) variety ‘Chinese Spring’. At low temperatures, asynapsis and chromosome univalence have been observed before in Chinese Spring lines lacking the long arm of chromosome 5D (5DL), which led to the proposal that 5DL carries a gene (Ltp1) that stabilises wheat chromosome pairing at low temperatures. In the current study, Chinese Spring wild type and 5DL interstitial deletion mutant plants were exposed to low temperature in a controlled environment room during a period from premeiotic interphase to early meiosis I. A 5DL deletion mutant was identified whose meiotic chromosomes exhibit extremely high levels of asynapsis and chromosome univalence at metaphase I after 7 days at 13 °C, suggesting that Ltp1 is deleted in this mutant. Immunolocalisation of the meiotic proteins ASY1 and ZYP1 on ltp1 mutants showed that low temperature results in a failure to complete synapsis at pachytene. KASP genotyping revealed that the ltp1 mutant has a 4-Mb deletion in 5DL. Of 41 genes within this deletion region, the strongest candidate for the stabilisation of chromosome pairing at low temperatures is the meiotic recombination gene Dmc1. The ltp1 mutants were subsequently treated at 30 °C for 24 h during meiosis and exhibited a reduced number of crossovers and increased univalence, though to a lesser extent than at 13 °C. We therefore renamed our ltp1 mutant ‘ttmei1’ (temperature-tolerant meiosis 1) to reflect this additional loss of high temperature tolerance.

Distinct Functions in Regulation of Meiotic Crossovers for DNA Damage Response Clamp Loader Rad24(Rad17) and Mec1(ATR) Kinase.

The number and distribution of meiotic crossovers (COs) are highly regulated, reflecting the requirement for COs during the first round of meiotic chromosome segregation. CO control includes CO assurance and CO interference, which promote at least one CO per chromosome bivalent and evenly-spaced COs, respectively. Previous studies revealed a role for the DNA damage response (DDR) clamp and the clamp loader in CO formation by promoting interfering COs and interhomolog recombination, and also by suppressing ectopic recombination. In this study, we use classical tetrad analysis of Saccharomyces cerevisiae to show that a mutant defective in RAD24, which encodes the DDR clamp loader (RAD17 in other organisms), displayed reduced CO frequencies on two shorter chromosomes (III and V), but not on a long chromosome (chromosome VII). The residual COs in the rad24 mutant do not show interference. In contrast to rad24, mutants defective in the ATR kinase homolog Mec1, including a mec1 null and a mec1 kinase-dead mutant, show slight or few defects in CO frequency. On the other hand, mec1 COs show defects in interference, similar to the rad24 mutant. Our results support a model in which the DDR clamp and clamp-loader proteins promote interfering COs by recruiting pro-CO Zip, Mer, and Msh proteins to recombination sites, while the Mec1 kinase regulates CO distribution by a distinct mechanism. Moreover, CO formation and its control are implemented in a chromosome-specific manner, which may reflect a role for chromosome size in regulation.

Assessing by Modeling the Consequences of Increased Recombination in Recurrent Selection of Oryza sativa and Brassica rapa.

Meiotic recombination generates genetic diversity but in most species the number of crossovers per meiosis is limited. Previous modeling studies showed that increasing recombination can enhance response to selection. However, such studies did not assume a specific method of modifying recombination. Our objective was to test whether two methods used to increase recombination in plants could increase genetic gain in a population undergoing recurrent selection such as in genomic selection programs. The first method, in Oryza sativa, used a mutant of anti-crossover genes, increasing global recombination without affecting the recombination landscape shape. The second one used the ploidy level of a cross between Brassica rapa and Brassica napus, increasing recombination especially in pericentromeric regions. Our modeling framework used these recombination landscapes and sampled quantitative trait loci positions from the actual gene distributions. We simulated selection programs with initially a cross between two inbred lines, for two species. Increased recombination enhanced the response to selection. The amount of enhancement in the cumulative gain largely depended on the species and the number of quantitative trait loci (2, 10, 20, 50, 200 or 1000 per chromosome). Genetic gains were increased up to 30% after 20 generations. Furthermore, increasing recombination in cold regions was the most effective: the gain was larger by 25% with the first method and 34% with the second one in B. rapa, and 12% compared to 16% in O. sativa. In summary, increased recombination enhances the genetic gain in long-term selection programs, with visible effects after four to five generations.

Meiotic arrest occurs most frequently at metaphase and is often incomplete in azoospermic men

To establish which meiotic checkpoints are activated in males with severe spermatogenic impairment to improve phenotypic characterization of meiotic defects. Retrospective observational study. University medical center research laboratory and andrology clinic. Forty-eight patients with confirmed spermatogenic impairment (Johnsen scores 3-6) and 15 controls (Johnsen score 10). None. Quantitative assessment of immunofluorescent analyses of specific markers to determine meiotic entry, chromosome pairing, progression of DNA double-strand break repair, crossover formation, formation of meiotic metaphases, metaphase arrest, and spermatid formation, resulting in a novel classification of human meiotic arrest types. Complete metaphase arrest was observed most frequently (27%), and the patients with the highest frequency of apoptotic metaphases also displayed a reduction in crossover number. Incomplete metaphase arrest was observed in 17% of the patients. Only four patients (8%) displayed a failure to complete meiotic chromosome pairing leading to pachytene arrest. Two new types of meiotic arrest were defined: premetaphase and postmetaphase arrest (15% and 13%, respectively). Meiotic arrest in men occurs most frequently at meiotic metaphase. This arrest can be incomplete, resulting in low numbers of spermatids, and often occurs in association with reduced crossover frequency. The phenotyping approach described here provides mechanistic insights to help identify candidate infertility genes and to assess genotype-phenotype correlations in individual cases.

CRL4 regulates recombination and synaptonemal complex aggregation in the Caenorhabditiselegans germline.

To maintain the integrity of the genome, meiotic DNA double strand breaks (DSBs) need to form by the meiosis-specific nuclease Spo11 and be repaired by homologous recombination. One class of products formed by recombination are crossovers, which are required for proper chromosome segregation in the first meiotic division. The synaptonemal complex (SC) is a protein structure that connects homologous chromosomes during meiotic prophase I. The proper assembly of the SC is important for recombination, crossover formation, and the subsequent chromosome segregation. Here we identify the components of Cullin RING E3 ubiquitin ligase 4 (CRL4) that play a role in SC assembly in Caenorhabditis elegans. Mutants of the CRL4 complex (cul-4, ddb-1, and gad-1) show defects in SC assembly manifested in the formation of polycomplexes (PCs), impaired progression of meiotic recombination, and reduction in crossover numbers. PCs that are formed in cul-4 mutants lack the mobile properties of wild type SC, but are likely not a direct target of ubiquitination. In C. elegans, SC assembly does not require recombination and there is no evidence that PC formation is regulated by recombination as well. However, in one cul-4 mutant PC formation is dependent upon early meiotic recombination, indicating that proper assembly of the SC can be diminished by recombination in some scenarios. Lastly, our studies suggest that CUL-4 deregulation leads to transposition of the Tc3 transposable element, and defects in formation of SPO-11-mediated DSBs. Our studies highlight previously unknown functions of CRL4 in C. elegans meiosis and show that CUL-4 likely plays multiple roles in meiosis that are essential for maintaining genome integrity.

Interspecific introgression mediates adaptation to whole genome duplication

Adaptive gene flow is a consequential phenomenon across all kingdoms. Although recognition is increasing, there is no study showing that bidirectional gene flow mediates adaptation at loci that manage core processes. We previously discovered concerted molecular changes among interacting members of the meiotic machinery controlling crossover number upon adaptation to whole-genome duplication (WGD) in Arabidopsis arenosa. Here we conduct a population genomic study to test the hypothesis that adaptation to WGD has been mediated by adaptive gene flow between A. arenosa and A. lyrata. We find that A. lyrata underwent WGD more recently than A. arenosa, suggesting that pre-adapted alleles have rescued nascent A. lyrata, but we also detect gene flow in the opposite direction at functionally interacting loci under the most extreme levels of selection. These data indicate that bidirectional gene flow allowed for survival after WGD, and that the merger of these species is greater than the sum of their parts.

Molecular evolution of the meiotic recombination pathway in mammals.

Meiotic recombination shapes evolution and helps to ensure proper chromosome segregation in most species that reproduce sexually. Recombination itself evolves, with species showing considerable divergence in the rate of crossing-over. However, the genetic basis of this divergence is poorly understood. Recombination events are produced via a complicated, but increasingly well-described, cellular pathway. We apply a phylogenetic comparative approach to a carefully selected panel of genes involved in the processes leading to crossovers-spanning double-strand break formation, strand invasion, the crossover/non-crossover decision, and resolution-to reconstruct the evolution of the recombination pathway in eutherian mammals and identify components of the pathway likely to contribute to divergence between species. Eleven recombination genes, predominantly involved in the stabilization of homologous pairing and the crossover/non-crossover decision, show evidence of rapid evolution and positive selection across mammals. We highlight TEX11 and associated genes involved in the synaptonemal complex and the early stages of the crossover/non-crossover decision as candidates for the evolution of recombination rate. Evolutionary comparisons to MLH1 count, a surrogate for the number of crossovers, reveal a positive correlation between genome-wide recombination rate and the rate of evolution at TEX11 across the mammalian phylogeny. Our results illustrate the power of viewing the evolution of recombination from a pathwayperspective.

Analysis of Learning and Memory Ability in an Alzheimer's Disease Mouse Model using the Morris Water Maze.

A Morris water maze (MWM) experiment forces experimental animals to swim and learn to find a platform hidden in the water. It is widely used in scientific research to assess the learning and memory of animals. Due to the extensive use of the MWM test, visual experimental protocols are essential for researchers. This manuscript uses the latest studies to introduce the protocol of the MWM test. Alzheimer' Disease (AD) is characterized by a progressive loss of memory and cognitive function. An alternative and complementary treatment used for AD is Manual Acupuncture (MA). To assess the learning and memory ability of AD model mice, the MWM test was conducted. The visible platform trial, hidden platform trial, probe trial, and reversal trial of MWM were used to evaluate spatial learning and memory ability. In the visible platform trial, the swimming speed and escape latency of mice in different groups was not significantly different. In the hidden platform and reversal trials, the AD group showed a long escape latency. The escape latency decreased significantly after the MA treatment. Low platform crossover number and the proportion of time in the SW quadrant in the probe trial increased after the MA treatment (p < 0.05 or p < 0.01). The results of the MWM tests suggest that MA can effectively improve the spatial learning and memory abilities of AD model mice. Rigorous experimental operations provided assurance of the reliability of the results.

USING GA FOR EVOLVING WEIGHTS IN NEURAL NETWORKS

This article aims at studying the behavior of different types of crossover operators in the performance of Genetic Algorithm. We have also studied the effects of the parameters and variables (crossover probability (pc), mutation probability (pm), population size (pop-size) and number of generation (NG)) for controlling the algorithm. This research accumulated most of the types of crossover operators these types are implemented on evolving weights of Neural Network problem. The article investigates the role of crossover in GAs with respect to this problem, by using a comparative study between the iteration results obtained from changing the parameters values (crossover probability, mutation rate, population size and number of generation). From the experimental results, the best parameters values for the Evolving Weights of XOR-NN problem are NG = 1000, pop-size = 50, pm = 0.001, pc = 0.5 and the best operator is Line Recombination crossover.

How many times should a cluster randomized crossover trial cross over?

Trial planning requires making efficient yet practical design choices. In a cluster randomized crossover trial, clusters of subjects cross back and forth between implementing the control and intervention conditions over the course of the trial, with each crossover marking the start of a new period. If it is possible to set up such a trial with more crossovers, a pertinent question is whether there are efficiency gains from clusters crossing over more frequently, and if these gains are substantial enough to justify the added complexity and cost of implementing more crossovers. We seek to determine the optimal number of crossovers for a fixed trial duration, and then identify other highly efficient designs by allowing the total number of clusters to vary and imposing thresholds on maximum cost and minimum statistical power. Our results pertain to trials with continuous recruitment and a continuous primary outcome, with the treatment effect estimated using a linear mixed model. To account for the similarity between subjects' outcomes within a cluster, we assume a correlation structure in which the correlation decays gradually in a continuous manner as the time between subjects' measurements increases. The optimal design is characterized by crossovers between the control and intervention conditions with each successive subject. However, this design is neither practical nor cost-efficient to implement, nor is it necessary: the gains in efficiency increase sharply in moving from a two-period to a four-period trial design, but approach an asymptote for the scenarios considered as the number of crossovers continues to increase.

Centromere-Proximal Meiotic Crossovers in Drosophila melanogaster Are Suppressed by Both Highly Repetitive Heterochromatin and Proximity to the Centromere.

Crossovers are essential in meiosis of most organisms to ensure the proper segregation of chromosomes, but improper placement of crossovers can result in nondisjunction and aneuploidy in progeny. In particular, crossovers near the centromere can cause nondisjunction. Centromere-proximal crossovers are suppressed by what is termed the centromere effect, but the mechanism is unknown. Here, we investigate contributions to centromere-proximal crossover suppression in Drosophila melanogaster We mapped a large number of centromere-proximal crossovers, and find that crossovers are essentially absent from the highly repetitive (HR)-heterochromatin surrounding the centromere but occur at a low frequency within the less-repetitive (LR)-heterochromatic region and adjacent euchromatin. Previous research suggested that flies that lack the Bloom syndrome helicase (Blm) lose meiotic crossover patterning, including the centromere effect. Mapping of centromere-proximal crossovers in Blm mutants reveals that the suppression within the HR-heterochromatin is intact, but the distance-dependent centromere effect is lost. We conclude that centromere-proximal crossovers are suppressed by two separable mechanisms: an HR-heterochromatin effect that completely suppresses crossovers in the HR-heterochromatin, and the centromere effect, which suppresses crossovers with a dissipating effect with distance from the centromere.